In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's...In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.展开更多
Cooperative pursuit poses challenges across natural,social,and technical systems,particularly when decentralized,slow-speed pursuers attempt to capture a high-speed evader with limited observation.Most existing contri...Cooperative pursuit poses challenges across natural,social,and technical systems,particularly when decentralized,slow-speed pursuers attempt to capture a high-speed evader with limited observation.Most existing contributions place the focus on the greedy pursuit of the evader,overlooking potential collaborations among pursuers.To tackle this issue,a decisionmaking framework of multi-agent coordinated reciprocity formation pursuit(MACRFP)via deep reinforcement learning is introduced.This framework integrates the actor-critic algorithm with the coordinated reciprocity mechanism to enhance the capability of capturing a faster evader.Initially,a local perception model is created by utilizing a cellular network to simulate limitations caused by obstacles.Next,the formation coalition of pursuit is guided by the Cartesian Oval,enabling dispersed pursuers to create a siege against the faster evader.Furthermore,a coordinated reciprocity model based on the coordination graph and the attention-based graph neural networks is developed,addressing the global coordination problem by estimating a reciprocity coefficient to adjust agents'rewards.Numerical simulations demonstrate the emergence of cooperative behaviors in cooperative besiegement,target tracking,and intelligent interception during the pursuit,indicating that the proposed algorithm enhances the feasibility and effectiveness of capturing a fast-escaping target by integrating coordinated reciprocity and coalition formation.展开更多
Satellite communication plays an important role in 6G systems.However,satellite communication systems are more susceptible to intentional or unintentional interference signals than other communication systems because ...Satellite communication plays an important role in 6G systems.However,satellite communication systems are more susceptible to intentional or unintentional interference signals than other communication systems because of their working mechanism of transparent forwarding.For the purpose of eliminating the influence of interference,this paper develops an angle reciprocal interference suppression scheme based on the reconstruction of interferenceplus-noise covariance matrix(ARIS-RIN).Firstly,we utilize the reciprocity between the known beam central angle and the unknown signal arrival angle to estimate the angle of arrival(AOA)of desired signal due to the multi-beam coverage.Then,according to the priori known spatial spectrum distribution,the interferenceplus-noise covariance matrix(INCM)is reconstructed by integrating within the range except the direction of desired signal.In order to correct the estimation bias of the first two steps,the worst-case performance optimization technology is adopted in the process of solving the beamforming vector.Numerical simulation results show that the developed scheme:1)has a higher output signal-to-interference-plus-noise ratio(SINR)under arbitrary signal-to-noise ratio(SNR);2)still has good performance under small snapshots;3)is robuster and easier to be realized when comparing with minimum variance distortionless response(MVDR)and the traditional diagonal loading algorithms.展开更多
Optical non-reciprocity is a fundamental phenomenon in photonics.It is crucial for developing devices that rely on directional signal control,such as optical isolators and circulators.However,most research in this fie...Optical non-reciprocity is a fundamental phenomenon in photonics.It is crucial for developing devices that rely on directional signal control,such as optical isolators and circulators.However,most research in this field has focused on systems in equilibrium or steady states.In this work,we demonstrate a room-temperature Rydberg atomic platform where the unidirectional propagation of light acts as a switch to mediate time-crystalline-like collective oscillations through atomic synchronization.展开更多
基金Supported by the Natural Science Foundation of Sichuan Province(No.2023NSFSC0065)。
文摘In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.
基金supported by the National Natural Science Foundation of China(72371052,71871042)。
文摘Cooperative pursuit poses challenges across natural,social,and technical systems,particularly when decentralized,slow-speed pursuers attempt to capture a high-speed evader with limited observation.Most existing contributions place the focus on the greedy pursuit of the evader,overlooking potential collaborations among pursuers.To tackle this issue,a decisionmaking framework of multi-agent coordinated reciprocity formation pursuit(MACRFP)via deep reinforcement learning is introduced.This framework integrates the actor-critic algorithm with the coordinated reciprocity mechanism to enhance the capability of capturing a faster evader.Initially,a local perception model is created by utilizing a cellular network to simulate limitations caused by obstacles.Next,the formation coalition of pursuit is guided by the Cartesian Oval,enabling dispersed pursuers to create a siege against the faster evader.Furthermore,a coordinated reciprocity model based on the coordination graph and the attention-based graph neural networks is developed,addressing the global coordination problem by estimating a reciprocity coefficient to adjust agents'rewards.Numerical simulations demonstrate the emergence of cooperative behaviors in cooperative besiegement,target tracking,and intelligent interception during the pursuit,indicating that the proposed algorithm enhances the feasibility and effectiveness of capturing a fast-escaping target by integrating coordinated reciprocity and coalition formation.
基金supported by the National Natural Science Foundation of China under Grants No.61671367 and 62471381the Research Foundation of Science and Technology on Communication Networks Laboratory,and the National Key Laboratory of Wireless Communications Foundation under Grant No.IFN202401.
文摘Satellite communication plays an important role in 6G systems.However,satellite communication systems are more susceptible to intentional or unintentional interference signals than other communication systems because of their working mechanism of transparent forwarding.For the purpose of eliminating the influence of interference,this paper develops an angle reciprocal interference suppression scheme based on the reconstruction of interferenceplus-noise covariance matrix(ARIS-RIN).Firstly,we utilize the reciprocity between the known beam central angle and the unknown signal arrival angle to estimate the angle of arrival(AOA)of desired signal due to the multi-beam coverage.Then,according to the priori known spatial spectrum distribution,the interferenceplus-noise covariance matrix(INCM)is reconstructed by integrating within the range except the direction of desired signal.In order to correct the estimation bias of the first two steps,the worst-case performance optimization technology is adopted in the process of solving the beamforming vector.Numerical simulation results show that the developed scheme:1)has a higher output signal-to-interference-plus-noise ratio(SINR)under arbitrary signal-to-noise ratio(SNR);2)still has good performance under small snapshots;3)is robuster and easier to be realized when comparing with minimum variance distortionless response(MVDR)and the traditional diagonal loading algorithms.
基金supported by the National Natural Science Foundation of China (Grant No.12274131)the Innovation Program for Quantum Science and Technology (Grant No.2024ZD0300101)。
文摘Optical non-reciprocity is a fundamental phenomenon in photonics.It is crucial for developing devices that rely on directional signal control,such as optical isolators and circulators.However,most research in this field has focused on systems in equilibrium or steady states.In this work,we demonstrate a room-temperature Rydberg atomic platform where the unidirectional propagation of light acts as a switch to mediate time-crystalline-like collective oscillations through atomic synchronization.
